Suite exacte de Mayer-Vietoris d’une extension triangulaire - Bendiffalah, B. (MATHEMATICA SCANDINAVICA, 2008)
In this article, we complete the results published in [2] using new proofs: we obtain a more general long exact sequence for the extension groups Ext_T^* of the triangular algebra T=[smallmatrix A & M 0 & Bsmallmatrix]. One may find such a long exact sequence in the works of Palmér and Roos [22], [23], but only for very special instances of T-modules. This extra effort allows us to show that the well-known Hochschild cohomological exact sequence of Happel ([16] and, more generally,[8] and [20]) is just a particular instance of that of Palmér-Roos, even if it seems we really need an assumption on M (the same trick also appears for the homological version using the Tor ^T_* functor). With this method, we obtain a sensible improvement for the isomorphism of [3], which computes the Hochschild cohomology of triangular algebras in several cases. At the end of the article, we relate the Palmér-Roos exact sequence with the classical (i.e. topological) Mayer-Vietoris exact sequence.